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Hopf bifurcation analysis of two zooplankton-phytoplankton model with two delays

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  • Shi, Renxiang
  • Yu, Jiang

Abstract

We take the delays due to gestation of two kinds of zooplankton as parameters, the dynamics of a two zooplankton-phytoplankton model is studied, we discussed the dynamics under six conditions: (1) τ1=τ2=0,(2) τ1>0,τ2=0, (3) τ1=0,τ2>0, (4) τ1=τ2>0, (5) τ1 ∈ (0, τ10), τ2 > 0, (6) τ2 ∈ (0, τ20), τ1 > 0, the Hopf bifurcation about condition (5) should be studied by center manifold theorem and normal form. At last, some simulations are given to support our results

Suggested Citation

  • Shi, Renxiang & Yu, Jiang, 2017. "Hopf bifurcation analysis of two zooplankton-phytoplankton model with two delays," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 62-73.
    • Handle: RePEc:eee:chsofr:v:100:y:2017:i:c:p:62-73
    DOI: 10.1016/j.chaos.2017.04.044
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    References listed on IDEAS

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    1. Chakraborty, Subhendu & Roy, Shovonlal & Chattopadhyay, J., 2008. "Nutrient-limited toxin production and the dynamics of two phytoplankton in culture media: A mathematical model," Ecological Modelling, Elsevier, vol. 213(2), pages 191-201.
    2. Zhao, Jiantao & Wei, Junjie, 2009. "Stability and bifurcation in a two harmful phytoplankton–zooplankton system," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1395-1409.
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    Cited by:

    1. Zhao, Qiuyue & Liu, Shutang & Niu, Xinglong, 2019. "Dynamic behavior analysis of a diffusive plankton model with defensive and offensive effects," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 94-102.
    2. Barman, Binandita & Ghosh, Bapan, 2019. "Explicit impacts of harvesting in delayed predator-prey models," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 213-228.
    3. Zhao, Qiuyue & Liu, Shutang & Tian, Dadong, 2018. "Dynamic behavior analysis of phytoplankton–zooplankton system with cell size and time delay," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 160-168.

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